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Tutorial 4 – Answers to Critical Thinking Questions The worksheets are available in the tutorials and form an integral part of the learning outcomes and experience for this unit. Model 1: Atomic Orbitals and Quantum Numbers 1. 2. 3. 4. The angular momentum quantum number, l. n Possible l values Orbital labels 1 0 s 2 0 and 1 s and p respectively 3 0, 1 and 2 s, p and d respectively 4 0, 1, 2 and 3 s, p, d and f respectively l Possible ml values Orbital labels 0 0 1xs 1 1, 0, -1 3 × p {px, py, pz} 2 2, 1, 0, -1, -2 5×d 3 3, 2, 1, 0, -1, -2, -3 7×f s orbitals have no planar nodes. p orbitals have one planar node. d orbitals have two planar nodes. 5. The number of planar nodes is equal to the value of the angular momentum quantum number, l. 6. The 2s and 3pz orbitals both have one spherical node and 3dx2-y2 has none. In general, the number of spherical nodes is equal to n – l - 1. Model 2: Electronic Configurations in Atoms 7. a. The Aufbau principle: Orbitals are filled with electrons in order of energy with the lowest energy orbital being filled first. b. Pauli exclusion principle: no two electrons may have the same set of quantum numbers. Each orbital can accommodate no more than 2 electrons. These 2 electrons will have opposite spin (ms). c. Hund’s Rule: in a set of orbitals with the same energy, electrons may not be spin-paired until each orbital in the set contains one electron. 8. See figure. a. The Pauli exclusion principle means that a maximum of two electrons can occupy an s orbital. The electron configuration of carbon 1s2 2s3 2p1 has three electrons in 2s. Hund’s rule means that the three 2p orbitals must each be occupied before electrons can pair up. b. The configuration 1s2 2s2 2px2 has two electrons spin-paired in 2px with the 2py and 2pz empty. 9. 2 10. All s orbitals can only have a maximum of 2 electrons. 11. All p orbitals can only have a maximum of 6 electrons (= 3 x 2 for each degenerate orbital). 12. a) 1s22s22p63s23p44s1 – the 3p orbitals were not completely filled before electrons were added to 4s (violating the Aufbau principle). The correct configuration is 1s22s22p63s23p5 b) 1s22s22p63s23p7 – the maximum number of electrons in 3p is 6 (violating the Pauli exclusion principle). The correct configuration is 1s22s22p63s23p64s1 c) 1s22s22p63s23p63d2 – the 4s orbital has a lower energy than 3d, so it will be filled first (violating the Aufbau principle). The correct configuration is 1s22s22p63s23p64s2 d) 1s22s22p63s23p64s23d104p65s23f 2 – there is no 3f orbital. The only orbitals with a principal quantum number of 3 are s, p and d. The correct configuration is 1s22s22p63s23p64s23d104p65s24d 2 Model 3: Electronic Configurations in Atoms and Ions 13. 14. The 4s orbital comes before the 3d orbital. Because of electron shielding (which results from the different shapes of the s and d orbitals), the 4s orbital has lower energy than the 3d orbital. 15. Atom or ion Number of Number of Electron configuration protons electrons Cl 17 17 1s22s22p63s23p5 Noble gas configuration (shorthand electron configuration) [Ne]3s23p5 Ar 18 18 1s22s22p63s23p6 [Ar] K 19 19 1s22s22p63s23p64s1 [Ar]4s1 Ca 20 20 1s22s22p63s23p64s2 [Ar]4s2 Cl- 17 18 1s22s22p63s23p6 [Ar] K+ 19 18 1s22s22p63s23p6 [Ar] Ca2+ 20 18 1s22s22p63s23p6 2 6 2 6 [Ar] Zn 30 30 1s 2s 2p 3s 3p 4s 3d [Ar]4s23d10 Sr 38 38 1s22s22p63s23p64s23d104p65s2 [Kr]5s2 Sr2+ 38 36 1s22s22p63s23p64s23d104p6 [Kr] 16. Ar, Cl-, K+, Ca2+ 17. Kr, Rb+, Br-, Se218. Sr 19. K 20. Cl 21. Zn 2 2 10